McKay, Donald. "Front matter" Multimedia Environmental Models ...

A check should be made of the magnitude of f/P S , where P S is the solid or liquid
vapor pressure. When this ratio equals 1, saturation is achieved. When the ratio
exceeds 1, the chemical will precipitate as a pure phase, i.e., its solubility in air or
water is exceeded, and the fugacity will drop to the saturation value indicated by
the vapor pressure. Normally, the ratio is much less than unity.
Four processes are considered as shown in Figure 8.1: (1) diffusive exchange by
volatilization and the reverse absorption, (2) dry deposition of aerosols, (3) wet
dissolution of chemical, and (4) wet deposition of aerosols. In each case, a D value
(mol/Pa h) is used to characterize the rate, which is Df mol/h.
For diffusion, the two-resistance approach is used, and D values are deduced for
the air and water boundary layers,
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D A = k A A Z A D W = k W A Z W
where k A and k W are mass transfer coefficients with units of m/h, and A is area (m 2 ).
Illustrative values of 5 m/h for k A and 5 cm/h for k W can be used, but it should be
appreciated that environmental values can vary widely, especially with wind speed,
and a separate calculation may be needed for the situation being simulated.
The overall resistance (1/D V) is obtained by adding the series resistances (1/D) as
1/D V = 1/D A + 1/D W
The rate of vaporization is then f WD V, the rate of absorption is f AD V, and the net rate
of vaporization is D V(f W – f A). An overall mass transfer coefficient is also calculated.
For dry deposition, a dry deposition velocity U D of particles is used, a typical
value being 0.3 cm/s or 10 m/h. The total dry deposition rate is thus U Dv QA m 3 /h,
the corresponding D value D D is U Dv QAZ Q, and the rate is D Df A mol/h.
For wet dissolution, a rain rate is defined, usually in units of m/year, a typical
value being 0.5 m/year or 6 ¥ 10 –5 m/h, designated U R. The total rain rate is then
U RA (m 3 /h), the D value, D R, is U RAZ W, and the rate is D Rf A mol/h.
For wet aerosol deposition, a scavenging ratio Q is used, representing the volume
of air efficiently scavenged by rain of its aerosol content, per unit volume of rain.
A typical value of Q is 200,000. The volume of air scavenged per hour is thus U RAQ
(m 3 /h), which will contain U RAQv Q (m 3 /h) of aerosol (v Q is the volume fraction of
aerosol). The D value D Q is thus U RAQv QZ Q, and the rate is D Qf A (mol/h).
A washout ratio is often employed in such calculations. This is the dimensionless
ratio of concentration in rain to total concentration in air, usually on a volumetric
(g/m 3 rain per g/m 3 air) basis, but occasionally on a gravimetric (mg/kg per mg/kg)
basis. The total rate of chemical deposition in rain is (D R + D Q)f A; thus, the concentration
in the rain is (D R + D Q)f A/U RA or f A(Z W + Qv QZ Q) mol/m 3 . The total air
concentration is f A(Z A + v QZ Q), and therefore the volumetric washout ratio is (Z W +
Qv QZ Q)/(Z A + v QZ Q). The gravimetric ratio is smaller by the ratio of air to water
densities, i.e., approximately 1.2/1000. If the chemical is almost entirely aerosol
associated, as is the case with metals such as lead, the volumetric washout ratio
approaches Q. These washout ratios are calculated and can be compared to reported
values.